A particle whose speed is `50ms^(-1)` moves along the line from `A(2,1)` to `B(9,25)`. Find its velocity vector in the from of `ahat(i)+bhat(j)`.

Options

A. `(7hat(i)+24hat(j)) m//s`
B. `2(7hat(i)+24hat(j))m//s`
C. `4(7hat(i)+24hat(j))m//s`
D. `5(7hat(i)+24hat(j))m//s`

Answer

B

Explanation

`vec(V)= 50(hat(A)B)`
`vec(AB)= (9-2)hat(i)+(25-1)hat(j)=(7hat(i)+24hat(j))`
`|vec(AB)|= sqrt((7^(2))+(24)^(2))`
`hat(AB)= (7hat(i)+24hat(j))/sqrt((7^(2))+(24^(2)))=((7hat(i)+24hat(j)))/(25)`
`vec(V)= 50.((7hat(i)+24hat(j)))/(25)= 2(7hat(i)+24hat(j))m//s`